Solve 5sqrt{2}+sqrt{8}-7sqrt{18}

$$5 \sqrt{ 2 } + \sqrt{ 8 } -7 \sqrt{ 18 }$$

Evaluate

$$-14\sqrt{2}\approx -19.798989873$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$5\sqrt{2}+2\sqrt{2}-7\sqrt{18}$$

Combine 5\sqrt{2} and 2\sqrt{2} to get 7\sqrt{2}.

$$7\sqrt{2}-7\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$7\sqrt{2}-7\times 3\sqrt{2}$$

Multiply -7 and 3 to get -21.

$$7\sqrt{2}-21\sqrt{2}$$

Combine 7\sqrt{2} and -21\sqrt{2} to get -14\sqrt{2}.

$$-14\sqrt{2}$$